Hi,
I was wondering how increasing the power of an equation would transform a graph?
e.g
y=ln(x^2)+6
vs
y=ln(x^3)+6
what change does increasing the power have?
A major change is that the graph will be defined for negative x when x has an even power.
Note than the graph of ln(x) is only defined for positive x as you cannot take the logarithm of a negative number. But if you have $\displaystyle y=ln(x^2)$, the graph will be defined for both positive and negative x as a negative value of x will become positive once you square.
Also, the graph will become steeper, due to you taking the natural logarithm of a larger and larger number as you increase the power of x.